FYI....A few years back I was in the same position. The Flt. Ops Specialist explained that when DSA is in play, pilots have the option of using it or having the trip (or in your case portion of trip) dropped without pay. Because pilots have that option, legally the company can't touch a pilots DSA without permission. In my case they contacted me and asked what I preferred to do. Doctors note wasn't required back then, but I hear these days they require one at every opportunity.
Can you expense your co-pay for a managment required doctors visit?